Lactate metabolism plays a critical role in mammalian cell bioprocessing, influencing cellular performance and productivity. The transition from lactate production to consumption, known as lactate metabolic shift, is highly beneficial and has been shown to extend culture lifespan and enhance productivity, yet its molecular drivers remain poorly understood. Here, we have explored the mechanisms that underpin this metabolic shift through two case studies, illustrating environmental- and genetic-driven factors. We characterised these study cases at process, metabolic and transcriptomic levels. Our findings indicate that glutamine depletion coincided with the timing of the lactate metabolic shift, significantly affecting cell growth, productivity and overall metabolism. Transcriptome analysis revealed dynamic regulation the ATF4 pathway, involved in the amino acid (starvation) response, where glutamine depletion activates ATF4 gene and its targets. Manipulating ATF4 expression through overexpression and knockdown experiments showed significant changes in metabolism of glutamine and lactate, impacting cellular performance. Overexpression of ATF4 increased cell growth and glutamine consumption, promoting a lactate metabolic shift. In contrast, ATF4 downregulation decreased cell proliferation and glutamine uptake, leading to production of lactate without any signs of lactate shift. These findings underscore a critical role for ATF4 in regulation of glutamine and lactate metabolism, related to phasic patterns of growth during CHO cell culture. This study offers unique insight into metabolic reprogramming during the lactate metabolic shift and the molecular drivers that determine cell status during culture.

An intervention, such as a form of therapy or a diet program to lose weight, is perceived as effective by a person if that person experiences a change (in thoughts, emotions, behavior) following the intervention. Scientific and statistical processes evaluate intervention based on differences in change over time between those who do and do not experience the intervention. In this paper, we provide a new approach to mediation analysis in the two-group pretest-posttest designs that coincides with such within-person psychological experience of change. Our method, the treatment as moderator (TAM) approach, focuses on differences between two conditions (i.e., between those who do versus do not receive an intervention of some kind) in the indirect and direct effects of the passage of time on an outcome variable, with the indirect effect operating through change over time on a mediator. We provide an example of the analysis and interpretation using data from a study examining the mediating role of emotional impulsivity on the effect of an online intervention designed to reduce aggression, while describing implementation with the MEMORE macro available for SPSS and SAS as well as in a structural equation modeling framework using the lavaan package in R.

Mediation analysis is widely used to test and inform theory and debate about the mechanism(s) by which causal effects operate, quantitatively operationalized as an indirect effect in a mediation model. Most effects operate through multiple mechanisms simultaneously, and a mediation model is likely to be more realistic when it is specified to capture multiple mechanisms at the same time with the inclusion of more than one mediator in the model. This also allows an investigator to compare indirect effects to each other. After an overview of the mechanics of mediation analysis, we advocate formally comparing indirect effects in models that include more than one mediator, focusing on the important distinction between questions and claims about value (i.e., are two indirect effects the same number?) versus magnitude (i.e., are two indirect effects equidistant from zero or the same in strength?). After discussing the shortcomings of the conventional method for comparing two indirect effects in a multiple mediator model—which only answers a question about magnitude in some circumstances—we introduce several methods that, unlike the conventional approach, always answer questions about difference in magnitude. We illustrate the use of these methods and provide code that implements them in popular software. We end by summarizing simulation findings and recommending which method(s) to prefer when comparing like- and opposite-signed indirect effects.

This work provides a conceptual introduction to mediation, moderation, and conditional process analysis in psychological research. We discuss the concepts of direct effect, indirect effect, total effect, conditional effect, conditional direct effect, conditional indirect effect, and the index of moderated mediation index, while providing our perspective on certain analysis and interpretation confusions that sometimes arise in practice in this journal and elsewhere, such as reliance on the causal steps approach and the Sobel test in mediation analysis, misinterpreting the regression coefficients in a model that includes a product of variables, and subgroups mediation analysis rather than conditional process analysis when exploring whether an indirect effect depends on a moderator. We also illustrate how to conduct various analyses that are the focus of this paper with the freely-available PROCESS procedure available for SPSS, SAS, and R, using data from an experimental investigation on the effectiveness of personal or testimonial narrative messages in improving intergroup attitudes.

Cronbach's alpha (alpha) is a widely-used measure of reliability used to quantify the amount of random measurement error that exists in a sum score or average generated by a multi-item measurement scale. Yet methodologists have warned that alpha is not an optimal measure of reliability relative to its more general form, McDonald's omega (). Among other reasons, that the computation of is not available as an option in many popular statistics programs and requires items loadings from a confirmatory factor analysis (CFA) have probably hindered more widespread adoption. After a bit of discussion of alpha versus , we illustrate the computation of using two structural equation modeling programs (Mplus and AMOS) and the MBESS package for R. We then describe a macro for SPSS and SAS (OMEGA) that calculates in two ways without relying on the estimation of loadings or error variances using CFA. We show that it produces estimates of that are nearly identical to when using CFA-based estimates of item loadings and error variances. We also discuss the use of the OMEGA macro for certain forms of item analysis and brief form construction based on the removal of items from a longer scale.

Clinical psychological science is improved when it seeks to understand not only whether an effect exists but also how that effect operates and its boundary conditions. Mediation and moderation analysis are widely used in clinical psychological research to explore and test hypotheses about the mechanisms by which causal effects operate and the contingencies of those effects. Their integration as conditional process analysis allows for the examination of the contingencies of those mechanisms – for whom or in what circumstances a particular mechanism is in operation or whether it is strong as opposed to weak. This chapter reviews the fundamentals of mediation, moderation, and conditional process analysis using ordinary least squares regression, commenting along the way on good practice as well as various misunderstandings in circulation. It illustrates the application of these fundamentals and their implementation using the PROCESS macro for SPSS and SAS.

Behavioral scientists use mediation analysis to understand the mechanism(s) by which an effect operates and moderation analysis to understand the contingencies or boundary conditions of effects. Yet how effects operate (i.e., the mechanism at work) and their boundary conditions (when they occur) are not necessarily independent, though they are often treated as such. Conditional process analysis is an analytical strategy that integrates mediation and moderation analysis with the goal of examining and testing hypotheses about how mechanisms vary as a function of context or individual differences. In this article, we provide a conceptual primer on conditional process analysis for those not familiar with the integration of moderation and mediation analysis, while also describing some recent advances and innovations for the more experienced conditional process analyst. After overviewing fundamental modeling principles using ordinary least squares regression, we discuss the extension of these fundamentals to models with more than one mediator and more than one moderator. We describe a differential dominance conditional process model and overview the concepts of partial, conditional, and moderated moderated mediation. We also discuss multilevel conditional process analysis and comment on implementation of conditional process analysis in statistical computing software.

Research in communication and other social science disciplines that relies on measuring each member of a dyad on putative causes and effects can require complex analyses to illuminate how members of the dyad influence one another. Dyadic mediation analysis is a branch of mediation analysis that focuses on establishing the mechanism(s) by which mutual influence operates. Relying on the similarity between dyadic mediation analysis using structural equation modeling and mediation analysis with ordinary least squares regression, we developed MEDYAD, an easy-to-use computational tool for SPSS, SAS, and R that conducts dyadic mediation analysis with distinguishable dyadic data. MEDYAD implements the Actor-Partner Interdependence Model Extended to Mediation (APIMeM), as well as simpler and more complex dyadic mediation models. Bootstrapping methods are implemented for inferences about indirect effects. Additional features include methods for conducting all possible pairwise comparisons between indirect effects, heteroskedasticity-robust inference, and saving bootstrap estimates of parameters for further analysis.

Mediation of X's effect on Y through a mediator M is moderated if the indirect effect of X depends on a fourth variable. Hayes [(2015). An index and test of linear moderated mediation. Multivariate Behavioral Research, 50, 1-22. doi:10.1080/00273171.2014.962683] introduced an approach to testing a moderated mediation hypothesis based on an index of moderated mediation. Here, I extend this approach to models with more than one moderator. I describe how to test if X's indirect effect on Y is moderated by one variable when a second moderator is held constant (partial moderated mediation), conditioned on (conditional moderated mediation), or dependent on a second moderator (moderated moderated mediation). Examples are provided, as is a discussion of the visualization of indirect effects and an illustration of implementation in the PROCESS macro for SPSS and SAS.

PROCESS model 1, used for estimating, testing, and probing interactions in ordinary least squares regression, constrains focal predictor X’s linear effect on outcome variable Y to be linearly moderated by a single moderator W . In this document I describe how to hack PROCESS to get it to estimate a model that includes linear moderation by W of a quadratic effect of X on Y , and quadratic moderation by W of a linear effect of X on Y . Instructions are provided for the implementation of the pick-a-point and Johnson-Neyman techniques for probing interactions in models that combine quadratic nonlinearity and moderation. In all of the examples of moderation in Introduction to Moderation, Mediation, and Conditional Process Analysis (Hayes, 2018), effects are estimated as linear effects. In a model of the form Ŷ = iY +b1X +b2W +b3XW , X’s effect on Y is constrained to be linear, meaning that a one unit difference in X corresponds to the same estimated difference in Y regardless of where you start on X. Furthermore, this model presumes that any influence of W on X’s effect is also linear. That is, as W changes by one unit, X’s effect on Y is constrained to change by b3 units, regardless of where you start on W . As described in many treatments of regression analysis, in spite of its name, linear regression can be used to model effects that are nonlinear. For instance, OLS regression can be used to estimate the regression coefficients in a model of the form Ŷ = iY + b1X + b2X which is not the equation for a straight line but, rather, the equation for a curve—a parabolic or quadratic function. In this model, the steepness of the curve—how much it bends—as well as whether it curves upward (convex) or downward (concave) is determined by b2. A Andrew F. Hayes, Department of Psychology, The Ohio State University, Columbus, OH 43210 USA, hayes.338@osu.edu, www.afhayes.com. Learn more about the use of PROCESS for moderation analysis by taking a class from Andrew Hayes. See the public workshop schedule at www.processmacro.org/workshops.html c ⃝ COPYRIGHT 2017 BY ANDREW F. HAYES. DO NOT POST ONLINE. 2 test of significance for b2 can be used as a test of nonlinearity in the relationship between X and Y . The two hacks introduced here are not about how to model a nonlinear effect using PROCESS. Rather, this document describes how to use PROCESS to estimate and probe a moderation model in which one variable’s nonlinear effect is linearly moderated, or in which one variable’s linear effect is nonlinearly moderated. This can be done using PROCESS models 1 or 2 fairly easily, as will be seen. Although the hack is easy to describe, understanding what it is doing and how to interpret the results is considerably more complex, and so I first give some treatment to the required statistical background. For both hacks presented here, I rely on data from 340 respondents to the 2000 American National Election Study, which is a regular survey of the U.S. public taken prior to each federal election (see www.electionstudies.org). The outcome variable in both examples is political knowledge (PKNOW), operationalized as the number of questions (out of 22) that a participant answered correctly about various public officials and people running for office (such as their stance on various social issues, or the positions in government they currently occupy). The data also includes a measure of news use (NEWS), which is a 3-item index constructed as the average number of days per week respondents reported watching the local or national network news broadcast and reading the newspaper. The analyses also include the respondent’s age in years (AGE), his or her sex (SEX, coded 0 for females and 1 for males), and a measure of the respondent’s socioeconomic status, operationalized as the average of his or her standardized income and number of years of education (SES). Estimating and Probing Linear Moderation of a Quadratic Effect Is there a relationship between political knowledge (Y ) and news use (X)? Using Pearson’s correlation as an index of association, this correlation is positive (r = 0.18, p < 0.001), meaning that those who use these sources of news relatively more frequently are more knowledgeable about various political actors on the national and international stage. Furthermore, controlling for sex, age, and socioeconomic status in a multiple regression analysis, this relationship persists (partial r = 0.120, partial regression coefficient = 0.265, p < 0.05). Holding constant age, sex, and socioeconomic status, each additional day of news use per week translates into a difference of 0.265 units of political knowledge. This is not a particularly big effect in might seem, but it is also not particularly surprising that the effect is positive. This analysis and its interpretation assumes that the relationship between news use and political knowledge is linear. But maybe it isn’t. There are many forms that nonlinearity can take. We focus here on examining if the association can be better characterized with a quadratic function. This is accomplished by adding the square of news use to the model as an additional predictor (X2). Thus, continuing to use age (W ), sex (U1), and socioeconomic status (U2) as covariates, the model estimated is Y = iY + b1X + b2X + b3W + b4U1 + b5U2 + eY (1) In this model, the relationship between news use and age is modeled as quadratic. In a nonlinear model such as this, X’s effect on Y (θX→Y ) is, in geometric terms, the slope of c ⃝ COPYRIGHT 2017 BY ANDREW F. HAYES. DO NOT POST ONLINE. 3 the line tangent to the function at the point X, also called the instantaneous rate of change of Y . It is calculated as the first derivative of equation 1 with respect to X, which here is θX→Y = b1 + 2b2X (2) So the effect of X on Y , θX→Y , is itself a function of X in this model. Observe from equation 2 that if b2 is zero, then the effect of X on Y is b1, and therefore not a function of X. This is equivalent to saying that X’s effect is linear. If b2 is positive, this means that the relationship between X and Y is nonlinear and convex, but if b2 is negative, then the relationship is nonlinear and concave. The larger b2 in absolute value, the sharper the bend in the curve. A test of nonlinearity of this form can be conducted by estimating the model and determining whether b2 is statistically different from zero. This analysis can be accomplished using any OLS regression program. Doing so yields Ŷ = 7.168 + 1.372X − 0.156X2 + 0.022W + 1.720U1 + 2.472U2 and b2 is statistically different from zero, b2 = −0.156, p < .01. In terms of improvement in model fit, the multiple correlation increases from R2 = 0.320 when X2 is not in the model to R2 = 0.336 when X2 is added. This change in R2, ∆R2 = 0.016, is statistically significant, F (1, 334) = 7.879, p < .01. But we already knew this, as a hypothesis test for b2 in the regression analysis is mathematically equivalent to this hypothesis test for ∆R2. A picture almost always helps and rarely hinders interpretation. A visual representation of this model can be found Figure 1 panel A, which sets all the covariates to their sample means. As can be seen, the relationship between news use and political knowledge is concave, with a peak in knowledge among those more moderate in their news use. Those who use the news relatively little or relatively frequently are lower in knowledge, at least according to this model. Moderation of the Curvilinearity The prior analysis is all background for understanding linear moderation of a quadratic effect. If this quadratic relationship between X and Y is moderated by some variable W , that means that the curve linking X to Y depends on W . More specifically, does the extent of the bend in the function—its steepness or direction (convex or concave) depend linearly on W? In this example, W will be age, and I will illustrate the estimation of the linear moderation by age of the curvilinear effect of news use on political knowledge revealed in the prior analysis. Assuming W is either dichotomous or continuous, the standard approach described in various books on regression analysis that tackle such a complex modeling process (e.g., Aiken & West, 1991; Cohen, Cohen, West, & Aiken, 2003) is to estimate Y from X, X2, W , XW , and X2W . Additional predictors could be included in the model as covariates. In this example, W is no longer a covariate as before but is now a moderator variable, but sex and socioeconomic status are still covariates. The model we estimate to test moderation of the curvilinear relationship between news use and political knowledge by age is Ŷ = iY + b1X + b2X + b3W + b4XW + b5XW + b6U1 + b7U2 (3) c ⃝ COPYRIGHT 2017 BY ANDREW F. HAYES. DO NOT POST ONLINE. 4 News Use 7 6 5 4 3 2 1 0 P o li ti ca l K n o w le d g e 13

Marketing, consumer, and organizational behavior researchers interested in studying the mechanisms by which effects operate and the conditions that enhance or inhibit such effects often rely on statistical mediation and conditional process analysis (also known as the analysis of “moderated mediation”). Model estimation is typically undertaken with ordinary least squares regression-based path analysis, such as implemented in the popular PROCESS macro for SPSS and SAS (Hayes, 2013), or using a structural equation modeling program. In this paper we answer a few frequently-asked questions about the difference between PROCESS and structural equation modeling and show by way of example that, for observed variable models, the choice of which to use is inconsequential, as the results are largely identical. We end by discussing considerations to ponder when making the choice between PROCESS and structural equation modeling.

Researchers interested in testing mediation often use designs where participants are measured on a dependent variable Y and a mediator M in both of two different circumstances. The dominant approach to assessing mediation in such a design, proposed by Judd, Kenny, and McClelland (2001), relies on a series of hypothesis tests about components of the mediation model and is not based on an estimate of or formal inference about the indirect effect. In this paper we recast Judd et al.’s approach in the path-analytic framework that is now commonly used in between-participant mediation analysis. By so doing, it is apparent how to estimate the indirect effect of a within-participant manipulation on some outcome through a mediator as the product of paths of influence. This path analytic approach eliminates the need for discrete hypothesis tests about components of the model to support a claim of mediation, as Judd et al’s method requires, because it relies only on an inference about the product of paths— the indirect effect. We generalize methods of inference for the indirect effect widely used in between-participant designs to this within-participant version of mediation analysis, including bootstrap confidence intervals and Monte Carlo confidence intervals. Using this path analytic approach, we extend the method to models with multiple mediators operating in parallel and serially and discuss the comparison of indirect effects in these more complex models. We offer macros and code for SPSS, SAS, and Mplus that conduct these analyses.

Empirical communication scholars and scientists in other fields regularly use regression models to test moderation hypotheses. When the independent variable X and moderator M are dichotomous or continuous, the practice of testing a linearmoderation hypothesis using regression analysis by including the product of X and M in a model of dependent variable Y is widespread. However, many research designs include multicategorical independent variables or moderators, such as in an experiment with three or more versions of a stimulus where participants are randomly assigned to one of them. Researchers are less likely to receive training about how to properly test a moderation hypothesis using regression analysis in such a situation. In this tutorial, we explain how to test, visualize, and probe interactions involving a multicategorical variable using linear regression analysis. While presenting and discussing the fundamentalsfundamentals that are not software specific-we emphasize the use of the PROCESS macro for SPSS and SAS, as it greatly simplifies the computations and potential for error that exists when doing computations by hand or using spreadsheets based on formulas in existing books on this topic. We also introduce an iterative computational implementation of the Johnson-Neyman technique for finding regions of significance of the effect of a multicategorical independent variable when the moderator is continuous.

There have been numerous treatments in the clinical research literature about various design, analysis, and interpretation considerations when testing hypotheses about mechanisms and contingencies of effects, popularly known as mediation and moderation analysis. In this paper we address the practice of mediation and moderation analysis using linear regression in the pages of Behaviour Research and Therapy and offer some observations and recommendations, debunk some popular myths, describe some new advances, and provide an example of mediation, moderation, and their integration as conditional process analysis using the PROCESS macro for SPSS and SAS. Our goal is to nudge clinical researchers away from historically significant but increasingly old school approaches toward modifications, revisions, and extensions that characterize more modern thinking about the analysis of the mechanisms and contingencies of effects.

There has been an upsurge of interest in compressed workweek schedules because of the opportunities they provide for enhanced organizational efficiency and more balanced work and life roles for employees. This study tested a moderated mediation model of the effects of compressed work hours satisfaction on absenteeism with the purpose of exploring both the mediation effects of emotional exhaustion and physical health and the moderating effects of sex on this relationship. It utilized data drawn from a sample of 236 contact-centre service workers linked to absenteeism data collected for a period of 12months following the survey. Results indicated that compressed work hours satisfaction was associated with lower absenteeism and that this relationship was mediated sequentially through emotional exhaustion and physical health. Although the indirect effect of compressed work hours satisfaction on absenteeism through emotional exhaustion and physical health was not significantly different between women and men, the relationship between compressed work hours satisfaction and physical health was positive for women but not for men. The implications of these findings are discussed.

I describe a test of linear moderated mediation in path analysis based on an interval estimate of the parameter of a function linking the indirect effect to values of a moderator-a parameter that I call the index of moderated mediation. This test can be used for models that integrate moderation and mediation in which the relationship between the indirect effect and the moderator is estimated as linear, including many of the models described by Edwards and Lambert (2007) and Preacher, Rucker, and Hayes (2007) as well as extensions of these models to processes involving multiple mediators operating in parallel or in serial. Generalization of the method to latent variable models is straightforward. Three empirical examples describe the computation of the index and the test, and its implementation is illustrated using Mplus and the PROCESS macro for SPSS and SAS.